Bioresource Technology 175 (2015) 502–508
Contents lists available at ScienceDirect
Bioresource Technology journal homepage: www.elsevier.com/locate/biortech
Uncertainty analysis and global sensitivity analysis of techno-economic assessments for biodiesel production Zhang-Chun Tang a,b,⇑, Lu Zhenzhou a, Liu Zhiwen b, Xiao Ningcong b a b
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, Shanxi, China School of Mechatronics Engineering, University of Electronic Science and Technology of China, Chengdu 611731, Sichuan, China
h i g h l i g h t s Economical feasibility of biodiesel production with uncertainties was assessed. Uncertainty analysis and parameter screening was carried out. Global sensitivity analysis was performed using three efficient methods. Results identified influential parameters on the life cycle cost.
a r t i c l e
i n f o
Article history: Received 20 June 2014 Received in revised form 29 October 2014 Accepted 30 October 2014 Available online 6 November 2014 Keywords: Techno-economic assessments Life cycle cost Unit cost Uncertainty analysis Global sensitivity analysis
a b s t r a c t There are various uncertain parameters in the techno-economic assessments (TEAs) of biodiesel production, including capital cost, interest rate, feedstock price, maintenance rate, biodiesel conversion efficiency, glycerol price and operating cost. However, fewer studies focus on the influence of these parameters on TEAs. This paper investigated the effects of these parameters on the life cycle cost (LCC) and the unit cost (UC) in the TEAs of biodiesel production. The results show that LCC and UC exhibit variations when involving uncertain parameters. Based on the uncertainty analysis, three global sensitivity analysis (GSA) methods are utilized to quantify the contribution of an individual uncertain parameter to LCC and UC. The GSA results reveal that the feedstock price and the interest rate produce considerable effects on the TEAs. These results can provide a useful guide for entrepreneurs when they plan plants. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Conventional fossil fuels can produce many deleterious emissions when igniting in engines, including greenhouse gases, NOx, hydrocarbons and particulate matter, which have caused various harmful influences on the global climate and air quality (Höök and Tang, 2013; Yan et al., 2014). It is desired to find alternative clean, economic and easy-to-use energy sources in the industry, the transport system, etc. As a renewable fuel, biodiesel has many advantages over the conventional fossil fuels in terms of environmental friendliness (Kalam et al., 2011; Frey and Kim, 2009; Fontaras et al., 2009; Chen et al., 2010). Thus, biodiesel has attracted more and more attention, and the biodiesel industry is growing rapidly. Many studies have focused on ⇑ Corresponding author at: School of Mechatronics Engineering, University of Electronic Science and Technology of China, Chengdu 611731, Sichuan, China. Tel.: +86 028 61831750. E-mail address: [email protected] (Z.-C. Tang). http://dx.doi.org/10.1016/j.biortech.2014.10.162 0960-8524/Ó 2014 Elsevier Ltd. All rights reserved.
biodiesel production from various feedstocks, such as palm oil (Chen et al., 2010), Jatropha curcas L. (Yusuf et al., 2012), waste cooking oil (Zhang et al., 2003), soybean oil (You et al., 2008), castor oil (Santana et al., 2010) and vegetable oils (Apostolakou et al., 2009). In order to understand the economical feasibility of biodiesel production, many researchers have conducted valuable studies on the techno-economic assessments (TEAs) of biodiesel production (Delrue et al., 2012; Nagarajan et al., 2013; Haas et al., 2006; Lozada et al., 2010; Jegannathan et al., 2011; Sakai et al., 2009; Ong et al., 2012). They focused on the life cycle cost (LCC) and the unit cost (UC) of biodiesel production within a project’s lifetime under the assumptions that all of the parameters were deterministic. In practice, many unavoidable, uncertain sources exist in the TEAs of biodiesel production during the project’s lifetime (Sotoft et al., 2010), such as the variation of the feedstock and biodiesel prices (Busse et al., 2012) and the fluctuation of the interest rate (Mankiw, 2011). As revealed by Borgonovo and Peccati (2006) and Brownbridge et al. (2014), the uncertainties in
503
Z.-C. Tang et al. / Bioresource Technology 175 (2015) 502–508
the parameters may exert important effects on the investment projects. In order to decrease these effects, engineers may be interested in knowing the contribution that each parameter has produced on the output and, further, how this contribution can be quantified. Global sensitivity analysis (GSA) is a beneficial tool to estimate the contribution of an individual parameter to the output. In this paper, three available GSA methods are employed to quantify the contribution of an individual parameter to LCC and UC, i.e., the variance-based importance measure (Saltelli et al., 2004), the moment-independent importance measure (Borgonovo et al., 2011) and the entropy-based importance measure (Tang et al., 2013). The GSA results can serve as a reasonable guide to the identification of the important parameters and the unimportant ones, which can tell the engineers which parameters require attention. The variance-based importance measure (Saltelli et al., 2004) is the most popular GSA tool to test the sensitivity of the output with respect to the random inputs, and it employs the expected reduction in the output variance due to the elimination of the uncertainty in the individual random input to define the effect of the random input on the output. However, as summarized by Borgonovo et al. (2011), the variance-based importance measure may no longer be a computationally advantageous method in the presence of the correlated model inputs. Therefore, the momentindependent importance measure was originally proposed by Borgonovo et al. (2011) as an alternative to the variance-based one. This GSA approach employs the expected shift in the probability density function (PDF) of the output after eliminating the uncertainty in the individual random input to measure the effect. Based on the fact that entropy can measure the uncertainty in a random variable, the authors also proposed an entropy-based GSA method (Tang et al., 2013), which used the expected shift in the entropy to assess the contribution of an individual random input to the output. The three GSA methods can measure the contribution of an individual random input to the output from different physical meanings, i.e., the output variance, the output PDF and the output entropy. Therefore, a combination of them can give a more comprehensive measurement of the contribution of the individual random input to the output. The paper is organized as follows. Section 2 introduces the TEAs of a biodiesel production and three available GSA methods. Section 3 performs the uncertainty analysis and the global sensitivity analysis for the techno-economic assessments of a biodiesel production under uncertain parameters. Conclusions are given in Section 4.
LCC ¼ CC þ
2.1. Techno-economic assessments of biodiesel production from crude palm oil Ong et al. (2012) investigated the TEAs of a plant producing biodiesel from crude palm oil with deterministic parameters. Based on this study, LCC and UC are introduced in the following. Then, the variation range of an individual parameter is also provided. The LCC of biodiesel production from crude palm oil within the project’s lifetime is defined by:
ð1Þ
where LCC is the life cycle cost; CC indicates the capital cost; FC is the feedstock cost; OC denotes the operating cost; MC represents the maintenance cost; SV is the salvage value and BPC is the byproduct credit.
n X FCi þ OCi þ MC i i¼1
ð1 þ rÞi
n X SV BPCi ; n i ð1 þ rÞ i¼1 ð1 þ rÞ
ð2Þ
where n is the project’s lifetime, i.e., n = 20; r represents the interest rate, i.e., r e [4.44%, 13.53%] (TRADING ECONOMICS, 2014); FCi, OCi, MCi and BPCi are the feedstock cost, the operating cost, the maintenance cost and the byproduct credit of the ith year, respectively. The definitions of all of the items in Eq. (1) will be given. According to Ong et al., 2012, the annual biodiesel production capacity of the plant is 50 ktons, i.e., PC = 50ktons. As revealed by Ong et al. (2012), the capital cost of the plant with such production capacity varies from $9 million to $15 million, i.e., CC e [$9 million, $15 million]. The main cost of biodiesel production is FC (i.e., the cost of the crude palm oil), which usually accounts for 80–90% of LCC (Hitchcock, 2014) and is expressed by:
FC ¼
n n n X X FP PC1000 FP FU X CE FCi ¼ ¼ ; i i ð1 þ rÞ ð1 þ rÞ i¼1 i¼1 i¼1
ð3Þ
where FP is the feedstock price or the crude palm oil price, which varied from $200/ton to $1200/ton in the past twelve years, FP e[$200/ton, $1200/ton] (Ong et al., 2012); FU is the annual total feedstock consumption; CE represents the conversion efficiency from feedstock to biodiesel, which generally varies from 96% to 99%, i.e., CE e [96%, 99%] (Nagi et al., 2008). The total OC within the project’s lifetime in the form of the present value model yields, which usually comprises less than 15% of LCC (Duncan, 2003), is defined by:
OC ¼
n n X X OR PC 1000 OCi ¼ ; ð1 þ rÞi i¼1 i¼1
ð4Þ
where OR is the operating rate or the operating cost of per-ton biodiesel production. Here, the percentage that FC comprises in LCC takes the value of 80% (Hitchcock, 2014), and the percentage that OC comprises in LCC is 15% (Duncan, 2003). Because the feedstock price is FP e [$200/ton, $1200/ton] (Ong et al., 2012), the operating rate or the operating cost of per-ton biodiesel production can be approximated as OR e [$37.5/ton, $225/ton] by the feedstock price. The total MC within the project’s lifetime is formulated by:
MC ¼
2. Methods
LCC ¼ CC þ FC þ OC þ MC SV BPC;
Business and economics commonly employ the present value calculations to compare the cash flows at different times. Therefore, in the form of the present value, LCC is expressed by:
n n X X MR CC MCi ¼ ; i i¼1 i¼1 ð1 þ rÞ
ð5Þ
where MR denotes the maintenance rate. MR takes a value of 2% in the research of Ong et al., 2012, and it is 1% in the work of Haas et al., 2006. Here, MR varies from 1% to 2%, i.e., MR e [1%, 2%]. Salvage value (SV) is the remaining value of the components and the assets of the plant at the end of the project’s lifetime, which is defined by: n1
SV ¼ RC ð1 dÞ
n1
PWFn ¼
RC ð1 dÞ ð1 þ rÞn
;
ð6Þ
where d is the depreciation rate, i.e., d = 5%; n = 20 is the project’s lifetime of the plant; RC is the replacement cost, i.e., RC = $10 million (Ong et al., 2012); PWFn is the present worth factor in the year n. For the plant producing biodiesel from the crude palm oil, the byproduct credit comes from the sale of glycerol, which is yielded during biodiesel production. The total amount of the byproduct credit during the project’s lifetime is defined by:
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BPC ¼
n n X X GP GCF PC 106 BPCi ¼ ; ð1 þ rÞi i¼1 i¼1
ð7Þ
LCC PC 106 =q n
m m X X Vi þ V ij þ þ V 1;2;:::;m ; i¼1
where GP is the glycerol price, i.e., GP e [$0.08/kg, $0.2/kg] (Nanda et al., 2014); GCF represents the glycerol conversion factor, i.e., GCF = 0.0985 (Ong et al., 2012). Unit cost (UC) of biodiesel production from the crude palm oil is defined as the cost per-liter of the biodiesel during the project’s lifetime. Therefore, the definition can be given by:
UC ¼
VðYÞ ¼
ð8Þ
:
where q represents the density of the biodiesel, i.e., q = 0.95 kg/l; PC is the annual biodiesel production capacity, i.e., PC = 50ktons; n = 20 is the project’s lifetime. Some key input parameters are summarized in Table 1. Their ranges are also provided. The ranges of the capital cost (x1) (Ong et al., 2012), the interest rate (x2) (TRADING ECONOMICS, 2014), the operating rate (x3) (Hitchcock, 2014; Duncan, 2003; Ong et al., 2012), the feedstock price (x4) (Ong et al., 2012), the glycerol price (x5) (Nanda et al., 2014), the maintenance rate (x6) (Ong et al., 2012; Haas et al., 2006) and the biodiesel conversion efficiency (x7) (Nagi et al., 2008) are determined by the available data. All of the uncertain parameters follow the uniform distributions within their ranges. 2.2. Global sensitivity analysis using three methods Sensitivity analysis (SA) can be grouped into the local sensitivity analysis (LSA) and GSA (Haaker and Verheijen, 2004). LSA investigates how much the output is changed by the small variation of the random input around a reference point (such as the nominal value), which depends on the choice of the reference point. Instead, GSA measures the contribution of an individual random input to the output within the entire range space of the input, which is independent of the choice of the reference point. Three GSA methods used in this paper are briefly introduced. 2.2.1. Variance-based importance measure In general, the chosen model can be written in the form of Y = g(x1, x2, . . ., xm), where x1, x2, . . ., xm are random inputs, and Y is the output of the model. In this paper, Y is LCC or UC of biodiesel production from the crude palm oil, and x1, x2, . . ., xm represent the random inputs of the techno-economic assessments, including the capital cost, the interest rate, the operating rate, the feedstock price, the glycerol price, the maintenance rate and the biodiesel conversion efficiency. The total variance of the output can be decomposed into (Saltelli et al., 2004):
ð9Þ
16i x2 > x3 x1, x5. Based on the GSA results shown in Fig. 4, the important parameters and the unimportant parameters can be identified. The important parameters are x2, x4 and x3, while the unimportant parameters include x1 and x5. For these unimportant parameters, their uncertainties can be removed, and they can be fixed to any values within their variation ranges without considerably affecting LCC. Fig. 5 shows the original and conditional PDFs of LCC, in which the conditional PDF of LCC is obtained when the unimportant parameters x1 and x5 are fixed to their central values. The differences between the original PDF and the conditional PDF are very small, indicating that eliminating the uncertainties of the unimportant parameters does not considerably affect LCC. For the important parameters x2, x4 and x3, Fig. 6 further shows the original and conditional PDFs of the LCC when x2, x4 and x3 are fixed to their central values. Fig. 6 reveals that the elimination of the uncertainties in the important parameters will lead to a distinct change of LCC variance. Another observation is that eliminating the uncertainties of the important parameters can shorten the variation range of LCC. For example, Fig. 6c shows that the original range of LCC (units: USD) is [0.2, 9.8] 108, while the conditional range of LCC becomes [2.4, 6.5] 108 after eliminating the uncertainty in x4. The previous results reveal that more attention should be paid to the important parameters including x2 (the interest rate), x3 (the operating rate) and x4 (the feedstock price or the crude palm oil price). But the uncertainties in other unimportant parameters can be ignored, and they can be fixed to any values within their ranges. 4. Conclusions The uncertainty and global sensitivity analysis have been carried out for the techno-economic assessments of a plant producing biodiesel from the crude palm oil with seven random input variables. The influence of parameters such as the capital cost, the interest rate, the operating rate, the feedstock price, the glycerol price, the maintenance rate and the biodiesel conversion efficiency on the life cycle cost has been considered. The results show that the interest rate and the feedstock price have a major influence on the life cycle cost. Acknowledgements Authors gratefully acknowledge the support of the National Natural Science Foundation of China under Grant Nos. NSFC 51405064 and NSFC 51375078, and the China Postdoctoral Science Foundation under contract numbers 2014M560707 and 2014M560708. References Apostolakou, A.A., Kookos, I.K., Marazioti, C., Angelopoulos, K.C., 2009. Technoeconomic analysis of a biodiesel production process from vegetable oils. Fuel Process. Technol. 90, 1023–1031. Borgonovo, E., Castaings, W., Tarantola, S., 2011. Moment independent importance measures: new results and analytical test cases. Risk Anal. 31, 404–428. Borgonovo, E., Peccati, L., 2006. Uncertainty and global sensitivity analysis in the evaluation of investment projects. Int. J. Prod. 104, 62–73. Botev, Z.I., Grotowski, J.F., Kroese, D.P., 2010. Kernel density estimation via diffusion. Ann. Stat. 38, 2916–2957. Brownbridge, G., Azadi, P., Smallbone, A., Bhave, A., Taylor, B., Kraft, M., 2014. The future viability of algae-derived biodiesel under economic and technical uncertainties. Bioresour. Technol. 151, 166–173.
Busse, S., Brümmer, B., Ihle, R., 2012. Price formation in the German biodiesel supply chain: a Markov-switching vector error-correction modeling approach. Agric. Econ. 43, 545–560. Chen, K.S., Lin, Y.C., Hsieh, L.T., Lin, L.F., Wu, C.C., 2010. Saving energy and reducing pollution by use of emulsified palm-biodiesel blends with bio-solution additive. Energy 35, 2043–2048. Dai, H., Wang, W., 2009. Application of low-discrepancy sampling method in structural reliability analysis. Struct. Saf. 31, 55–64. Delrue, F., Setier, P.A., Sahut, C., Cournac, L., Roubaud, A., Peltier, G., Froment, A.K., 2012. An economic, sustainability, and energetic model of biodiesel production from microalgae. Bioresour. Technol. 111, 191–200. Duncan, J., 2003. Costs of biodiesel production. Available at: (accessed October 18, 2014). Fontaras, G., Karavalakis, G., Kousoulidou, M., Tzamkiozis, T., Ntziachristos, L., Bakeas, E., 2009. Effects of biodiesel on passenger car fuel consumption, regulated and non-regulated pollutant emissions over legislated and real world driving cycles. Fuel 88, 1608–1617. Frey, H.C., Kim, K., 2009. In-use measurement of the activity, fuel use, and emissions of eight cement mixer trucks operated on each of petroleum diesel and soybased B20 biodiesel. Transp. Res. Part D Transp. Environ. 14, 585–592. Haaker, M.P.R., Verheijen, P.J.T., 2004. Local and global sensitivity analysis for a reactor design with parameter uncertainty. Chem. Eng. Res. Des. 82, 591– 598. Haas, M.J., McAloon, A.J., Yee, W.C., Foglia, T.A., 2006. A process model to estimate biodiesel production costs. Bioresour. Technol. 97, 671–678. Hitchcock, G., 2014. The Economics of Biofuel Production and Use. Available at: (accessed October 18, 2014). Höök, M., Tang, X., 2013. Depletion of fossil fuels and anthropogenic climate change – a review. Energy Policy 52, 797–809. Jegannathan, K.R., Eng-Seng, C., Ravindra, P., 2011. Economic assessment of biodiesel production: comparison of alkali and biocatalyst processes. Renew Sust. Energy Rev. 15, 745–751. Kalam, M.A., Masjuki, H.H., Jayed, M.H., Liaquat, A.M., 2011. Emission and performance characteristics of an indirect ignition diesel engine fuelled with waste cooking oil. Energy 36, 397–402. Lozada, I., Islas, J., Grande, G., 2010. Environmental and economic feasibility of palm oil biodiesel in the Mexican transportation sector. Renew Sust. Energy Rev. 14, 486–492. Mankiw, N.G., 2011. Principles of Economics, sixth ed. Western Cengage Learning. Montgomery, D.C., 2013. Design and Analysis of Experiments, eighth ed. John Wiley & Sons. Nagarajan, S., Chou, S.K., Cao, S., Wu, C., Zhou, Z., 2013. An updated comprehensive techno-economic analysis of algae biodiesel. Bioresour. Technol. 145, 150– 156. Nagi, J., Ahmed, S.K., Nagi, F., 2008. Palm biodiesel an alternative green renewable energy for the energy demands of the future. Int. Conf. Constr. Build. Technol., 79–94. Nanda, M.R., Yuan, Z., Qin, W., Poirier, M.A., Chunbao, X., 2014. Purification of crude glycerol using acidification: effects of acid types and product characterization. Austin J. Chem. Eng. 1, 1–7. Ong, H.C., Mahlia, T.M.I., Masjuki, H.H., Honnery, D., 2012. Life cycle cost and sensitivity analysis of palm biodiesel production. Fuel 98, 131–139. Saltelli, A., Tarantolla, A., Campolongo, F., Ratto, M., 2004. Sensitivity Analysis in Practice. Wiley, New York. Sakai, T., Kawashima, A., Koshikawa, T., 2009. Economic assessment of batch biodiesel production processes using homogeneous and heterogeneous alkali catalysts. Bioresour. Technol. 100, 3268–3276. Santana, G.C.S., Martins, P.F., da Silva, N.D., Batistella, C.B., Made, R., Maciel, M.R.W., 2010. Simulation and cost estimate for biodiesel production using castor oil. Chem. Eng. Res. Des. 88, 626–632. Sotoft, L.F., Rong, B.G., Christensen, K.V., Norddahl, B., 2010. Process simulation and economical evaluation of enzymatic biodiesel production plant. Bioresour. Technol. 101, 5266–5274. Tang, Z.C., Lu, Z.Z., Jiang, B., Wang, P., Zhang, F., 2013. Entropy-based importance measure for uncertain model inputs. AIAA J. 51, 2319–2334. TRADING ECONOMICS, 2014. Malaysia interest rate 1996-2014. Available at: (accessed October 9, 2014). Yan, Y.J., Li, X., Wang, G.L., Gui, X.H., Li, G.L., Su, F., Wang, X.F., Liu, T., 2014. Biotechnological preparation of biodiesel and its high-valued derivatives: a review. Appl. Energy 113, 1614–1631. You, Y.D., Shie, J.L., Chang, C.Y., Huang, S.H., Pai, C.Y., Yu, Y.H., Chang, C.H., 2008. Economic cost analysis of biodiesel production: case in soybean oil. Energy Fuel 22, 182–189. Yusuf, N.N.A.N., Kamarudin, S.K., Yaakob, Z., 2012. Overview on the production of biodiesel from Jatropha curcas L. by using heterogenous catalysts. Biofuels Bioprod. Biorefin. 6, 319–334. Zhang, Y., Dube, M.A., McLean, D.D., Kates, M., 2003. Biodiesel production from waste cooking oil: 2. Economic assessment and sensitivity analysis. Bioresour. Technol. 90, 229–240.
Contents lists available at ScienceDirect
Bioresource Technology journal homepage: www.elsevier.com/locate/biortech
Uncertainty analysis and global sensitivity analysis of techno-economic assessments for biodiesel production Zhang-Chun Tang a,b,⇑, Lu Zhenzhou a, Liu Zhiwen b, Xiao Ningcong b a b
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, Shanxi, China School of Mechatronics Engineering, University of Electronic Science and Technology of China, Chengdu 611731, Sichuan, China
h i g h l i g h t s Economical feasibility of biodiesel production with uncertainties was assessed. Uncertainty analysis and parameter screening was carried out. Global sensitivity analysis was performed using three efficient methods. Results identified influential parameters on the life cycle cost.
a r t i c l e
i n f o
Article history: Received 20 June 2014 Received in revised form 29 October 2014 Accepted 30 October 2014 Available online 6 November 2014 Keywords: Techno-economic assessments Life cycle cost Unit cost Uncertainty analysis Global sensitivity analysis
a b s t r a c t There are various uncertain parameters in the techno-economic assessments (TEAs) of biodiesel production, including capital cost, interest rate, feedstock price, maintenance rate, biodiesel conversion efficiency, glycerol price and operating cost. However, fewer studies focus on the influence of these parameters on TEAs. This paper investigated the effects of these parameters on the life cycle cost (LCC) and the unit cost (UC) in the TEAs of biodiesel production. The results show that LCC and UC exhibit variations when involving uncertain parameters. Based on the uncertainty analysis, three global sensitivity analysis (GSA) methods are utilized to quantify the contribution of an individual uncertain parameter to LCC and UC. The GSA results reveal that the feedstock price and the interest rate produce considerable effects on the TEAs. These results can provide a useful guide for entrepreneurs when they plan plants. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Conventional fossil fuels can produce many deleterious emissions when igniting in engines, including greenhouse gases, NOx, hydrocarbons and particulate matter, which have caused various harmful influences on the global climate and air quality (Höök and Tang, 2013; Yan et al., 2014). It is desired to find alternative clean, economic and easy-to-use energy sources in the industry, the transport system, etc. As a renewable fuel, biodiesel has many advantages over the conventional fossil fuels in terms of environmental friendliness (Kalam et al., 2011; Frey and Kim, 2009; Fontaras et al., 2009; Chen et al., 2010). Thus, biodiesel has attracted more and more attention, and the biodiesel industry is growing rapidly. Many studies have focused on ⇑ Corresponding author at: School of Mechatronics Engineering, University of Electronic Science and Technology of China, Chengdu 611731, Sichuan, China. Tel.: +86 028 61831750. E-mail address: [email protected] (Z.-C. Tang). http://dx.doi.org/10.1016/j.biortech.2014.10.162 0960-8524/Ó 2014 Elsevier Ltd. All rights reserved.
biodiesel production from various feedstocks, such as palm oil (Chen et al., 2010), Jatropha curcas L. (Yusuf et al., 2012), waste cooking oil (Zhang et al., 2003), soybean oil (You et al., 2008), castor oil (Santana et al., 2010) and vegetable oils (Apostolakou et al., 2009). In order to understand the economical feasibility of biodiesel production, many researchers have conducted valuable studies on the techno-economic assessments (TEAs) of biodiesel production (Delrue et al., 2012; Nagarajan et al., 2013; Haas et al., 2006; Lozada et al., 2010; Jegannathan et al., 2011; Sakai et al., 2009; Ong et al., 2012). They focused on the life cycle cost (LCC) and the unit cost (UC) of biodiesel production within a project’s lifetime under the assumptions that all of the parameters were deterministic. In practice, many unavoidable, uncertain sources exist in the TEAs of biodiesel production during the project’s lifetime (Sotoft et al., 2010), such as the variation of the feedstock and biodiesel prices (Busse et al., 2012) and the fluctuation of the interest rate (Mankiw, 2011). As revealed by Borgonovo and Peccati (2006) and Brownbridge et al. (2014), the uncertainties in
503
Z.-C. Tang et al. / Bioresource Technology 175 (2015) 502–508
the parameters may exert important effects on the investment projects. In order to decrease these effects, engineers may be interested in knowing the contribution that each parameter has produced on the output and, further, how this contribution can be quantified. Global sensitivity analysis (GSA) is a beneficial tool to estimate the contribution of an individual parameter to the output. In this paper, three available GSA methods are employed to quantify the contribution of an individual parameter to LCC and UC, i.e., the variance-based importance measure (Saltelli et al., 2004), the moment-independent importance measure (Borgonovo et al., 2011) and the entropy-based importance measure (Tang et al., 2013). The GSA results can serve as a reasonable guide to the identification of the important parameters and the unimportant ones, which can tell the engineers which parameters require attention. The variance-based importance measure (Saltelli et al., 2004) is the most popular GSA tool to test the sensitivity of the output with respect to the random inputs, and it employs the expected reduction in the output variance due to the elimination of the uncertainty in the individual random input to define the effect of the random input on the output. However, as summarized by Borgonovo et al. (2011), the variance-based importance measure may no longer be a computationally advantageous method in the presence of the correlated model inputs. Therefore, the momentindependent importance measure was originally proposed by Borgonovo et al. (2011) as an alternative to the variance-based one. This GSA approach employs the expected shift in the probability density function (PDF) of the output after eliminating the uncertainty in the individual random input to measure the effect. Based on the fact that entropy can measure the uncertainty in a random variable, the authors also proposed an entropy-based GSA method (Tang et al., 2013), which used the expected shift in the entropy to assess the contribution of an individual random input to the output. The three GSA methods can measure the contribution of an individual random input to the output from different physical meanings, i.e., the output variance, the output PDF and the output entropy. Therefore, a combination of them can give a more comprehensive measurement of the contribution of the individual random input to the output. The paper is organized as follows. Section 2 introduces the TEAs of a biodiesel production and three available GSA methods. Section 3 performs the uncertainty analysis and the global sensitivity analysis for the techno-economic assessments of a biodiesel production under uncertain parameters. Conclusions are given in Section 4.
LCC ¼ CC þ
2.1. Techno-economic assessments of biodiesel production from crude palm oil Ong et al. (2012) investigated the TEAs of a plant producing biodiesel from crude palm oil with deterministic parameters. Based on this study, LCC and UC are introduced in the following. Then, the variation range of an individual parameter is also provided. The LCC of biodiesel production from crude palm oil within the project’s lifetime is defined by:
ð1Þ
where LCC is the life cycle cost; CC indicates the capital cost; FC is the feedstock cost; OC denotes the operating cost; MC represents the maintenance cost; SV is the salvage value and BPC is the byproduct credit.
n X FCi þ OCi þ MC i i¼1
ð1 þ rÞi
n X SV BPCi ; n i ð1 þ rÞ i¼1 ð1 þ rÞ
ð2Þ
where n is the project’s lifetime, i.e., n = 20; r represents the interest rate, i.e., r e [4.44%, 13.53%] (TRADING ECONOMICS, 2014); FCi, OCi, MCi and BPCi are the feedstock cost, the operating cost, the maintenance cost and the byproduct credit of the ith year, respectively. The definitions of all of the items in Eq. (1) will be given. According to Ong et al., 2012, the annual biodiesel production capacity of the plant is 50 ktons, i.e., PC = 50ktons. As revealed by Ong et al. (2012), the capital cost of the plant with such production capacity varies from $9 million to $15 million, i.e., CC e [$9 million, $15 million]. The main cost of biodiesel production is FC (i.e., the cost of the crude palm oil), which usually accounts for 80–90% of LCC (Hitchcock, 2014) and is expressed by:
FC ¼
n n n X X FP PC1000 FP FU X CE FCi ¼ ¼ ; i i ð1 þ rÞ ð1 þ rÞ i¼1 i¼1 i¼1
ð3Þ
where FP is the feedstock price or the crude palm oil price, which varied from $200/ton to $1200/ton in the past twelve years, FP e[$200/ton, $1200/ton] (Ong et al., 2012); FU is the annual total feedstock consumption; CE represents the conversion efficiency from feedstock to biodiesel, which generally varies from 96% to 99%, i.e., CE e [96%, 99%] (Nagi et al., 2008). The total OC within the project’s lifetime in the form of the present value model yields, which usually comprises less than 15% of LCC (Duncan, 2003), is defined by:
OC ¼
n n X X OR PC 1000 OCi ¼ ; ð1 þ rÞi i¼1 i¼1
ð4Þ
where OR is the operating rate or the operating cost of per-ton biodiesel production. Here, the percentage that FC comprises in LCC takes the value of 80% (Hitchcock, 2014), and the percentage that OC comprises in LCC is 15% (Duncan, 2003). Because the feedstock price is FP e [$200/ton, $1200/ton] (Ong et al., 2012), the operating rate or the operating cost of per-ton biodiesel production can be approximated as OR e [$37.5/ton, $225/ton] by the feedstock price. The total MC within the project’s lifetime is formulated by:
MC ¼
2. Methods
LCC ¼ CC þ FC þ OC þ MC SV BPC;
Business and economics commonly employ the present value calculations to compare the cash flows at different times. Therefore, in the form of the present value, LCC is expressed by:
n n X X MR CC MCi ¼ ; i i¼1 i¼1 ð1 þ rÞ
ð5Þ
where MR denotes the maintenance rate. MR takes a value of 2% in the research of Ong et al., 2012, and it is 1% in the work of Haas et al., 2006. Here, MR varies from 1% to 2%, i.e., MR e [1%, 2%]. Salvage value (SV) is the remaining value of the components and the assets of the plant at the end of the project’s lifetime, which is defined by: n1
SV ¼ RC ð1 dÞ
n1
PWFn ¼
RC ð1 dÞ ð1 þ rÞn
;
ð6Þ
where d is the depreciation rate, i.e., d = 5%; n = 20 is the project’s lifetime of the plant; RC is the replacement cost, i.e., RC = $10 million (Ong et al., 2012); PWFn is the present worth factor in the year n. For the plant producing biodiesel from the crude palm oil, the byproduct credit comes from the sale of glycerol, which is yielded during biodiesel production. The total amount of the byproduct credit during the project’s lifetime is defined by:
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BPC ¼
n n X X GP GCF PC 106 BPCi ¼ ; ð1 þ rÞi i¼1 i¼1
ð7Þ
LCC PC 106 =q n
m m X X Vi þ V ij þ þ V 1;2;:::;m ; i¼1
where GP is the glycerol price, i.e., GP e [$0.08/kg, $0.2/kg] (Nanda et al., 2014); GCF represents the glycerol conversion factor, i.e., GCF = 0.0985 (Ong et al., 2012). Unit cost (UC) of biodiesel production from the crude palm oil is defined as the cost per-liter of the biodiesel during the project’s lifetime. Therefore, the definition can be given by:
UC ¼
VðYÞ ¼
ð8Þ
:
where q represents the density of the biodiesel, i.e., q = 0.95 kg/l; PC is the annual biodiesel production capacity, i.e., PC = 50ktons; n = 20 is the project’s lifetime. Some key input parameters are summarized in Table 1. Their ranges are also provided. The ranges of the capital cost (x1) (Ong et al., 2012), the interest rate (x2) (TRADING ECONOMICS, 2014), the operating rate (x3) (Hitchcock, 2014; Duncan, 2003; Ong et al., 2012), the feedstock price (x4) (Ong et al., 2012), the glycerol price (x5) (Nanda et al., 2014), the maintenance rate (x6) (Ong et al., 2012; Haas et al., 2006) and the biodiesel conversion efficiency (x7) (Nagi et al., 2008) are determined by the available data. All of the uncertain parameters follow the uniform distributions within their ranges. 2.2. Global sensitivity analysis using three methods Sensitivity analysis (SA) can be grouped into the local sensitivity analysis (LSA) and GSA (Haaker and Verheijen, 2004). LSA investigates how much the output is changed by the small variation of the random input around a reference point (such as the nominal value), which depends on the choice of the reference point. Instead, GSA measures the contribution of an individual random input to the output within the entire range space of the input, which is independent of the choice of the reference point. Three GSA methods used in this paper are briefly introduced. 2.2.1. Variance-based importance measure In general, the chosen model can be written in the form of Y = g(x1, x2, . . ., xm), where x1, x2, . . ., xm are random inputs, and Y is the output of the model. In this paper, Y is LCC or UC of biodiesel production from the crude palm oil, and x1, x2, . . ., xm represent the random inputs of the techno-economic assessments, including the capital cost, the interest rate, the operating rate, the feedstock price, the glycerol price, the maintenance rate and the biodiesel conversion efficiency. The total variance of the output can be decomposed into (Saltelli et al., 2004):
ð9Þ
16i x2 > x3 x1, x5. Based on the GSA results shown in Fig. 4, the important parameters and the unimportant parameters can be identified. The important parameters are x2, x4 and x3, while the unimportant parameters include x1 and x5. For these unimportant parameters, their uncertainties can be removed, and they can be fixed to any values within their variation ranges without considerably affecting LCC. Fig. 5 shows the original and conditional PDFs of LCC, in which the conditional PDF of LCC is obtained when the unimportant parameters x1 and x5 are fixed to their central values. The differences between the original PDF and the conditional PDF are very small, indicating that eliminating the uncertainties of the unimportant parameters does not considerably affect LCC. For the important parameters x2, x4 and x3, Fig. 6 further shows the original and conditional PDFs of the LCC when x2, x4 and x3 are fixed to their central values. Fig. 6 reveals that the elimination of the uncertainties in the important parameters will lead to a distinct change of LCC variance. Another observation is that eliminating the uncertainties of the important parameters can shorten the variation range of LCC. For example, Fig. 6c shows that the original range of LCC (units: USD) is [0.2, 9.8] 108, while the conditional range of LCC becomes [2.4, 6.5] 108 after eliminating the uncertainty in x4. The previous results reveal that more attention should be paid to the important parameters including x2 (the interest rate), x3 (the operating rate) and x4 (the feedstock price or the crude palm oil price). But the uncertainties in other unimportant parameters can be ignored, and they can be fixed to any values within their ranges. 4. Conclusions The uncertainty and global sensitivity analysis have been carried out for the techno-economic assessments of a plant producing biodiesel from the crude palm oil with seven random input variables. The influence of parameters such as the capital cost, the interest rate, the operating rate, the feedstock price, the glycerol price, the maintenance rate and the biodiesel conversion efficiency on the life cycle cost has been considered. The results show that the interest rate and the feedstock price have a major influence on the life cycle cost. Acknowledgements Authors gratefully acknowledge the support of the National Natural Science Foundation of China under Grant Nos. NSFC 51405064 and NSFC 51375078, and the China Postdoctoral Science Foundation under contract numbers 2014M560707 and 2014M560708. References Apostolakou, A.A., Kookos, I.K., Marazioti, C., Angelopoulos, K.C., 2009. Technoeconomic analysis of a biodiesel production process from vegetable oils. Fuel Process. Technol. 90, 1023–1031. Borgonovo, E., Castaings, W., Tarantola, S., 2011. Moment independent importance measures: new results and analytical test cases. Risk Anal. 31, 404–428. Borgonovo, E., Peccati, L., 2006. Uncertainty and global sensitivity analysis in the evaluation of investment projects. Int. J. Prod. 104, 62–73. Botev, Z.I., Grotowski, J.F., Kroese, D.P., 2010. Kernel density estimation via diffusion. Ann. Stat. 38, 2916–2957. Brownbridge, G., Azadi, P., Smallbone, A., Bhave, A., Taylor, B., Kraft, M., 2014. The future viability of algae-derived biodiesel under economic and technical uncertainties. Bioresour. Technol. 151, 166–173.
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